The case was registered only recently in the Secretariat Police Station in Islamabad on the orders of the high court.
A police officer told PTI that the case was dropped over the issue of jurisdiction.
"The drone attack was carried out in tribal areas that do not fall in the jurisdiction of the capital police," he said.
He said that the issue of aggrieved party was transferred to Federally Administered Tribal Areas (FATA) Secretariat, which is responsible for affairs of the tribal region.
Also Read
The strikes by the CIA-operated spy planes against militants have been controversial due to many civilian deaths in the attacks.
The police station had earlier refused Khan's request to register the FIR but finally lodged it after Islamabad High Court (IHC) asked it to do so.
Banks left Pakistan in 2010 after his cover was blown when Khan threatened to sue the CIA and others for USD 500 million over the deaths of his 18-year-old son and brother in the December 31, 2009 drone strike.